King Solomon's Dilemma and Behavioral Economics

When the tale of King Solomon's dilemma was first told to me as a kid, I was (like most people, no doubt) left marvelling at Solomon's brilliant solution to a rather difficult predicament.

But then I grew up and made the unfortunate choice of pursuing a graduate degree in economics. My mind was left rotted to the point where I could no longer appreciate what most other people continued to believe was the self-evident wisdom of Solomon.

The problem with Solomon's "solution" is that it adopts what in modern parlance would be labeled a "behavioral approach." In other words, the solution relies heavily on the assumption that people are "irrational" in a particular sense. It turns out to be easy to be a wise philosopher king when one assumes that everyone else is irrational. Perhaps this is why so many aspiring philosopher kings today want to replace conventional economic theory with what they call "behavioral economics."

Let's think about this. The "mechanism" (game) designed by Solomon proposes to split the baby in two (sounds "fair" at least). One women screams out "No! Let the other have the whole baby instead." The other woman coldly agrees to the solution. The real mother is revealed in the obvious manner. What is not so obvious is why the false mother could not have anticipated this outcome; a more clever woman would have simply mimicked the behavior of the true mother. Instead, the false mother fails to make this calculation (and instead adopts a simple "behavioral" strategy; which is just a fancy label for irrational behavior).

Now, perhaps there really are "irrational" people like the false mother. But would you be willing to stake a baby's life on this assumption? Even if this mechanism worked out one time, could we reasonably expect it to work in the future (would people not learn from the outcome and tailor their strategies accordingly?). If you believe that people are fundamentally irrational in this sense, then you will make a fine behavioral economist (and a poor philosopher king).

So what is the solution to Solomon's dilemma?

One approach might be to adopt the Coase theorem, which states that if transaction costs are zero, then an arbitrary assignment of property rights will lead to the efficient solution. That is, Solomon could just have assigned the baby at random to one or the other woman. If it fell into the hands of the false mother, the true mother (who presumably values the baby more) could then purchase the baby (from the one who values it less). In other words, if there are gains to trade (as would obviously exist in this case), then these gains will be realized--if transaction costs are zero.

The problem with this approach is that transaction costs are obviously not zero (these costs could arise, for example, if the true value of the baby by both women is private information). Moreover, this "solution" violates what most people would consider to be a principle of "fairness" (why should the true mother pay for her own baby?). The Coase theorem is a fascinating theorem, but it should not be applied as a solution to the problem at hand; the theorem simply states what one could expect to happen IF transaction costs are zero. In fact, the Coase theorem should be interpreted as explaining precisely why various institutions emerge to handle the problem of resource allocation in a world where transaction costs are not zero.

One such solution was offered by Solomon. But I have already highlighted the problem with his proposed institution (or mechanism). Another possible solution was offered by William Vickery: a sealed-bid second-price auction (or a Vickery auction). Assume, as seems reasonable in this case, that only the two mothers know the true value they attach to the baby. A Vickery auction would have both mothers submitting sealed bids for the baby. The woman with the highest bid would then win the auction, but pay the second-highest bid.

This solution is clever because the amount that either woman expects to pay is independent of their actual bid. Accordingly, neither one of them have an incentive to misrepresent how much they really value the baby. If the true mother values the baby more, she will win the auction (it would not be rational for the false mother to bid more than what the baby is worth to her).

Clever indeed. But there is still a problem associated with this solution. In particular, it requires that the true mother actually pay for her baby. Leaving issues of "fairness" aside, a more relevant problem may be that this mother does not have the resources to make the requisite payment. (It is absolutely critical that the payment be forthcoming; if Solomon could not credibly commit to collecting the payment, then rational players will understand this limitation and alter their strategies accordingly).

One solution might be to let the women offer themselves as indentured servants. This sounds feasible and has the desirable property that the true mother gets her baby (she would presumably be happy to offer herself as Solomon's servant, if it means getting her baby). While this solution has its drawbacks, it seems to dominate Solomon's solution--something that risks having the baby split in two.

But is it possible to design a mechanism that "does the right thing" without any cost to the true mother? Several solutions have been proposed in the literature; but each with its own peculiar drawbacks. But I recently came across one proposed solution that seems quite clever; see Bid and Guess: A Nested Solution to King Solomon's Dilemma, by Cheng-Zhong Qin of UC Santa Barbara.

The idea as presented in Qin's paper seems a little more complicated than it needs to be (but I could be wrong). The basic idea, as I see it, is to have the women play a "participation game" just before playing a standard Vickery auction. We could set up the mechanism as follows.

First, Solomon informs the women of the Vickery auction that will be used to allocate the baby. Second, he informs each woman that the price of participating in the Vickery auction will be a half-life of servitude in some miserable occupation. The women are then asked to submit envelopes with ballots that are marked "yes" or "no" (yes, I am willing to participate; no I am not). If both women submit "yes," then the Vickery auction is played. If only one woman submits "yes," then the baby is allocated to her for free (the auction is not played). If neither woman submits "yes," then the baby is disposed of in some manner (perhaps in the King's service).

Now, put yourself in the place of first, the true mother and second, the false mother. How would you play the game? Would you say "yes" or "no?"

Theory suggests that the true mother will say "yes" to the participation game (she knows that she will get the baby if the auction is played; she will pay one half-life of servitude for participation, and the other half-life in payment for the baby). Likewise, the false mother will say "no." Why submit to a half-life of servitude when she knows that she will inevitably lose the subsequent auction? The false mother will rationally bow out of the bidding; she will choose not to participate. And the baby is allocated for free to the true mother.

Of course, this assumes that the people playing this game are "rational" in the sense that they understand the rules of the game and in the sense that they can anticipate how others are likely to play it. One of the great strengths of assuming rationality in this form is that the assumption can be applied as a general condition that prevails in any resource allocation problem. Its weakness is that people may not always possess this assumed degree of rationality.

But the alternative--the "behavioral approach"--suffers from an even greater problem. In particular, the policymaker must be aware of precisely how people are irrational in each and every given circumstance (a great loss in generality). There are an infinite number of ways in which people might be irrational; and the behavioral theorist is forced to choose among an infinite number of "behavioral rules" that he or she believes captures this irrationality in a plausible manner. The only hope that a behavioral theorist has for developing a general theory is in discovering that people are irrational in some systematic manner. But if the theorist can identify this systematic pattern of irrationality, it seems hard to know why people cannot discover it for themselves too. But then, it seems clearly in the interest of aspiring philosopher kings prefer to think of themselves as being systematically more rational than the subjects they study.

South Park on the Financial Crisis

Am winding down a two-week visit at the department of economics at Nanterre (Paris X). Paris is lovely, even at this time of year. And naturally, I have fallen in love...with the bakery next to my flat (a sure sign of old age, when one prefers to oggle a fresh baguette in a shop window, rather than the pretty Parisiennes walking down the street).

During my idle time (digestive phase), I surf the net for amusing/interesting pieces. Most of my searches have turned up idiotic musings by the likes of Buiter, DeLong, and comrade Anatole. But here now, I have finally found the jewel among the rot: an episode from South Park that draws on Monty Python's "The Life of Brian."

This is absolutely brilliant; a short clip is available here.

I wonder whether all the finger-pointers might recognize themselves? (I doubt it).

Goodbye, Homo Economicus

Here we have Anatole Kaletsky, giving us his version of the Buiter rant: Goodbye, Homo Economicus.

Who is Anatole Kaletsky? Evidently, he is an "economist." Well, more like a journalist-economist-consultant-forecaster. That is, he is a snake-oil salesman; which is to say, he is richer than you or I.

In this fine piece, Kaletsky argues that economists must take the blame for the current financial crisis. Well, not all economists, of course. Not economists like Kaletsky, for example. Not the "talking head" economists, or the economists who like to forecast things. The blame lies with academic economists...like me. Well, I am sorry. I am truly sorry for causing the crisis.

The fault lies with academics who plant crazy ideas into the minds of people (adults who cannot possibly be held responsible for what they learn). Crazy ideas like efficient markets, the glory of capitalism, blah, blah, blah. One can certainly see how these crazy ideas have manifested themselves as unbridled capitalism run amok (it is inconvenient here to observe that the financial sector is by far the most heavily regulated sector in any "well-developed" economy).

To flash his eruditeness, Kaletsky offers us the following quote from Keynes:

Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back.

I like this quote and agree with it. Kaletsky evidently believes that the economist is to blame for this; rather than the madmen who adopt their ideas. Evidently, Kaletsky must have skipped some classes at Cambridge. I see that Keynes (1923) also said:

The theory of economics does not furnish a body of settled conclusions immediately applicable to policy. It is a method rather than a doctrine, an apparatus of the mind, a technique of thinking which helps its possessor to draw correct conclusions.

This is something that Kaletsky evidently does not understand. He certainly shows none of the humility that academic economists demonstrate when it comes to understanding the world around them. For example, take a look at Kaletsky's bold predictions for the economy (made January 2008), Goodbye to all that: the worst is over for the global credit crunch.

His predictions are as follows:

[1] The global credit crisis is now almost over;
[2] There will be no U.S. recession;
[3] Stock markets around the world will rise in 2008;
[4] There will be a "decoupling" between the U.S. and Asia;
[5] The sterling will fall against every other major currency

Incredibly, every single one of his predictions failed to materialize. This takes an incredible amount of skill (generally, bullshit forecasts can expect to be correct 50% of the time). But I suppose that the fault here again lies with academic economists. Shame on all of you!

Larry Summers on Fear and Greed

I used to think that Larry Summers was a reasonable sort of fellow. By here is some evidence proving that spending too much time in administration and politics can rot even the best mind; see White House: Greed Will Help. Here are some quotes:

"In the past few years, we’ve seen too much greed and too little fear; too much spending and not enough saving; too much borrowing and not enough worrying," Summers said Friday in a speech to the Brookings Institution. "Today, however, our problem is exactly the opposite."

Borrowing, you see, is evidently linked to greed; especially if one borrows too much. I am reminded of university students who mindlessly accumulate too much student debt. The greedy bastards. Or of poor people mindlessly borrowing to finance a home purchase. The greedy SOBs. There is too much borrowing; too much spending; there is too much greed.

Saving, on the other hand, is evidently linked to fear. Fear is a virture (as in the fear of God). As when all those virtuous savers bid up the NASDAQ to 5000. Whoops; this doesn't sound right. Perhaps he means saving in virtuous assets, like government treasuries (backed by virtuous/coercive taxation; rather than the prospect of future cash flow from a successful enterprise). Yes, fear is a virture...unless there is too much fear. Then fear is bad.

To summarize then: greed is vice; fear is a virtue. Unless there is too much fear, which is not a virtue. Not enough greed is a virtue; but not a good virtue...which is to say it is a vice. I am getting confused. Let me consult the article again.

"While greed is no virtue, entrepreneurship and the search for opportunity is what we need today."

OK, this clears things up. Make no mistake: greed is no virtue. But we do need more of it at a time like this. So to sum up, greed (borrowing) is bad and fear (saving) is bad (unless there is not enough of either). In the world economy (a closed system), we know that borrowing = saving. And this proves that greed is always balanced by fear. Wait a second, I am confused again. Perhaps what we need is a "new generation" IS-PC-TR like model to help policymakers confront the difficult economic choices they face in balancing fear and greed.

Assume that the policymaker has a quadratic loss function in deviations of actual fear and greed around some socially optimal level of fear and greed (we will let Woodford provide the microfoundations for this social welfare function). Accordingly, let us write this loss function as,

L(t) = 0.5(f(t) - f)^(1/2) + 0.5(g(t) - g)^(1/2)

Here, (f,g) are the socially optimal levels of fear and greed. f(t) and g(t) are the prevailing levels of fear and greed at date t. The policymaker wishes to minimize the fluctuations in fear and greed around their socially optimal levels.

We need more restrictions. Let's see. It seems natural to suppose that fear is influenced in some manner by endogenous variables and an exogenous shock; let's say

f(t) = a*f(t-1) - b*y(t) + e(t)

where y(t) is the output gap; and e(t) is the shock (like a "fear" markup shock in New Keynesian models).

Greed, on the other hand, is influenced by the interest rate and exogenous factors; e.g.,

g(t) = c*g(t-1) - d*r(t) + u(t)

where r(t) is the interest rate, set by monetary policy. Lowering r(t), the way Greenspan did, results in an increase in greed. Seems right.

Now, the policymaker wishes to choose an interest rate rule that miminizes the loss function, given the stochastic processes (estimated as the residuals from a mindless OLS or VAR) governing the fear and greed shocks.

Yes, I can see how the New Keynesian model, so widely used by central banks to justify the policies they follow, will no doubt be replaced by my formalization of Summer's hypothesis. The implications for policy design are likely to prove equally enlightening. Anyone care to coauthor this paper with me? Fame (or notoriety) is virtually guaranteed!

CDO Squared, Anyone?

Along with Martin Hellwig, I think that the other bright light in the field of finance is Gary Gorton of Yale. He has published several very interesting papers on historical banking panic episodes; see here. He gives a detailed account of the subprime mortgage market and the financial innovations associated with it in his paper entitled "The Panic of 2007."

In this paper, he describes the nuances of subprime mortgages; in particular, how their particular design made them very sensitive to the underlying asset price (unlike conventional mortgages). Evidently, this was by design (there was no other way for creditors to make money servicing this particular demographic).

He goes on to describe how these subprime mortgages were packaged into mortgage backed securities (MBS). This is a common form of securitization (although, the design of these also differed in a subtle, but important manner, from standard securitizations). As with other securitizations, mortgages were pooled and then tranches were formed; e.g., a senior tranche, a mezzanine tranche, and an equity tranche.

This type of securitization has an economic rationale. Higher rated tranches can be sold to insurance companies and pension funds (whose liabilities are longer term in nature). In principle, the originator of the MBS should could then hold on to the junior (equity) tranche. This gives the originator the incentive to construct a sound MBS; as the originator is the first in line to potential losses.

What I do not understand is what followed. These MBS were then used as backing for new securities, called Collateralized Debt Obligations (CDOs). For example, the mezzanine tranche of the MBS (rated BBB) would then be divided into senior, mezzanine, and junior tranches. The mezzanine tranche of this CDO would then be divided again into senior, mezzanine, and junior tranches (a CDO squared). The senior tranches of the CDO squareds would be assigned AAA ratings!

I do not understand the economic rationale for this further subdivision of the original MBS. I presume that there must be one (perhaps to get around some government regulations?). Is there an expert in finance out there that can help me out? I have had little luck in finding anything that explains the motivation for why CDOs exist.

Martin Hellwig on the Financial Crisis

Tired of all that sanctimonious drivel spewing from the likes of Dani Rodrik and Willem Buiter? Head aching from the cacophony of shrill voices rejoicing at the end of the world?

Then consult the good doctor Martin Hellwig; see here.

He also has a very nice article entitled "International Contagion: The Result of Information or Rhetoric?" that is well worth reading.

Would be interested to hear what people think.

Brad DeLong: Bad Economist, Good Historian?

In the lead up to his debate with Michele Boldrin on fiscal policy, DeLong cannot hide his sense of pride in proclaiming that "I am not a macroeconomist; I am an economic historian."

As the debate unfolded, he (unintentionally, no doubt) supplied us with ample evidence confirming his lack of theoretical training (to be more precise, his reliance on those "really useful ad hoc models" that appear sufficient to organize anyone's thinking on macroeconomic phenomena).

At one point, for example, he presented some data showing that employment was falling even in states that were not heavily exposed to subprime mortgages. The implication we were presumably to draw from this fact is that the current downturn is nothing more than an old-fashioned decline in "aggregate demand" (the cause of which is conveniently ignored, as this requires some deep-thinking). The corollary is that a large government fiscal stimulus is obviously desirable to mitigate the (unexplained) decline in private-sector "demand."

There are, of course, competing theories that are consistent with what an historian (or econometrician) might interpret as an "exogenous decline in aggregate demand." Many of these theories are no more or less crazy than DeLong's preferred theory (his Econ 101 macroeconomics principles course notes). He apparently does not feel the need to temper his opinion by the humility that any good scientist should feel by the difficulty associated with discriminating among several competing hypotheses. Yes, there is no doubt that DeLong is a bad scientist.

But then, DeLong is not a scientist; he is a self-proclaimed historian. Someone who documents previously unknown facts and provides data that challenges preconceived notions. Someone like Joel Mokyr, for example (read his delightful The Lever of Riches). I am sure that DeLong has made useful contributions in his field (actually, I really enjoyed reading his piece on America's peacetime inflation). But I now have a little cloud of doubt over whether we should trust him even here.

I am not an economic historian; but I have done some reading on economic history. And in particular, I have done a fair bit of reading on Herbert Hoover; whose opinions and policies were shamelessly distorted by DeLong in his debate with Boldrin. Bob Murphy drives this point home splendidly. Consider, for example, what DeLong said:

"Now Prof. Boldrin is following a very old trail, all right, his trail was in fact the ruling theory behind the Hoover Administration's policies in the 1930s. And to quote from President Herbert Hoover's autobiography, during his administration economic policy was made by quote "the leave-it-alone liquidationists headed by my Secretary of the Treasury Mellon, who felt the government must keep its hands off the economy and let the slump liquidate itself."

Inexplicably, DeLong fails to inform his audience of what follows this quote in Hoover's autobiography:

"But other members of the Administration, also having economic responsibilities- Under Secretary of the Treasury Mills, Governor Young of the Reserve Board, Secretary of Commerce Lamont and Secretary of Agriculture Hyde--believed with me that we should use the powers of government to cushion the situation."

Any good (or honest) economic historian must know that Hoover was no laissez-faire apologist. As the world's foremost mining engineer at the turn of the last century, Hoover saw first-hand and disapproved strongly of the speculative manias that frequently arose in his industry. As head of the Belgian Relief effort of WW1, Hoover orchestrated a massive interventionist effort that literally saved the lives of tens of millions Europeans. As Secretary of Commerce in the 1920s, he lobbied frequently for banking reform (lobbying efforts that were repeatedly quashed by the Governor of New York; none other than FDR) and warned of a growing mania in stock prices. His interventionist tendencies in the early days of the Great Depression were frequently blocked by the Democratic Congress (FDR accused him of being a reckless spendthrift). Most of "FDRs" New Deal policies were lifted wholesale from Hoover himself. If you do not believe this, then consider this quote from one of FDR's early advisors (Raymond Moley, writing in Newsweek, June 14, 1948):

"When we all burst into Washington...we found every essential idea (of the New Deal) enacted in the 100-day Congress in the Hoover administration itself. The essentials of the NRA, the PWA, the emergency relief setup were all there. Even the AAA was known to the Department of Agriculture. Only the TVA and the Securities Act was drawn from other sources. The RFC, probably the greatest recovery agency, was of course a Hoover measure, passed long before the inauguration."

Is DeLong a good economic historian? I'll let you be the judge.